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Dynamics of Feeder Cattle Basis and Price Slides
Kole Swanser Ph.D. Candidate
North Carolina State University
Selected Paper prepared for presentation at the Agricultural & Applied
Economics Association’s 2013 AAEA & CAES Joint Annual Meeting,
Washington, DC, August 4-6, 2013.
Copyright 2013 by Kole Swanser. All rights reserved. Readers may make verbatim copies of this
document for non-commercial purposes by any means, provided this copyright notice appears on
all such copies.
Dynamics of Feeder Cattle Basis and Price Slides
Abstract
This study examines the dynamics of the relationship between per pound prices for feeder cattle
at different sale weights. The feeder cattle “price slide” relationship, as it is commonly known,
is influenced by fluctuations in the output price for slaughter cattle and the input price of feed
corn. I empirically test predictions about price slide dynamics that are derived from a two-input
derived demand model for slaughter cattle. Empirical analysis is conducted using an extensive
dataset of feeder cattle transactions.
1
I. Introduction
Changing cattle prices contribute to fluctuations in the value of beef cattle and represent
an important source of risk for all involved in the cattle industry. Futures markets can be useful
for managing this risk only to the extent that cattle basis – defined as the difference between the
per pound price for a standardized feeder cattle futures contract and the cash price for any
specific group (lot) of cattle – can be understood and predicted. Two of the most important
factors that influence feeder cattle prices and values are the price of finished cattle and the cost
of feed inputs. The former represents output price – it measures the value of fed cattle that have
reached a slaughter weight of around 1,250 pounds at the end of their production cycle. The
latter represents the most substantial variable cost component of producing finished cattle from
lighter feeder cattle.
Prices of standardized futures contracts for fed slaughter cattle and corn (a primary cattle
feeding input) are determined almost continuously on the Chicago Mercantile Exchange (CME).
In the same way that the value of a farmer’s standing crop depends on current futures price for
the commodity that can only be delivered after harvest, the value of a group of cattle today
depends on fed cattle prices in the future, when those animals are ready for slaughter. After
adjusting for time to slaughter, changes in fed cattle prices indicate changes in the expected
ending value of lighter weight cattle. The impact of corn prices on the value of unfinished cattle
is more complex. Changes in the cost of corn (a proxy for feed input cost) will have a disparate
effect on cattle according to weight. Since lighter animals require more feed to reach finishing
weight, the value of these animals is more sensitive to future feed costs. This has direct
implications for the risk associated with owning cattle. Specifically, lightweight cattle are more
exposed to value fluctuation resulting from corn price variability.
The fact that per pound prices for feeder cattle tend to decrease as sale weight increases is
well-known to market observers and has been studied and documented by agricultural
economists (Ehrich 1969, Buccola 1980, Marsh 1985, Dhuyvetter and Schroeder 2000). Within
the cattle industry, this price-weight relationship is commonly called the “price slide.” The slope
of the price slide is heavily influenced by the price of the feed inputs that will be used to add
weight to cattle. Constant changes in the shape of the cattle price slide reflect complex
interactions between dynamic markets for feed inputs and fed cattle and other feeder cattle price
2
determinants. Previous researchers have even documented extreme market conditions when per
pound prices for lightweight cattle have been discounted relative to heavier animals. These
unusual periods when the market exhibits an “inverted price slide” correspond to very high corn
prices relative to live cattle prices. Recent years have produced record high cattle and corn
prices and significant price fluctuations. We have also seen the rising importance of ethanol
production as a competing use for corn. These developments suggest that an updated analysis
using extensive current data may yield additional insights about these market dynamics.
My analysis of cattle and corn price dynamics begins by first developing predictions
about the relationship between futures price expectations and the cattle price slide using a two-
input slaughter cattle production model within a simple derived demand framework. I then
empirically test these predictions using a subset of data from a very large database of transaction-
level feeder cattle sales. This working paper concludes with a discussion about intended areas of
future research.
II. A Two-Input Derived Demand Model of Cattle Feeding
I generate predictions for the effects of cattle and corn prices on the slope of the price
slide using a simple two-input derived demand model.1 In this model, one finished steer for
slaughter is produced by combining one steer weighing 200 lbs. to 1,250 lbs. with the requisite
amount of a corn feed input.2 I make the simplifying assumption that cattle and corn are used in
fixed proportions, and that the quantity of corn input required can be calculated directly based on
the amount of weight gain required for the input steer to reach slaughter weight (assumed to be
exactly 1,250 lbs.).
The value of the output good, one finished steer, is determined by the market price of live
cattle. Factors that affect the market price of live cattle include the demand for live cattle, which
1 Two futures contracts for beef cattle are traded on the CME (Chicago Mercantile Exchange). The feeder cattle contract (FC) is for 650-850 pound steers. The live cattle futures contract (LC) is for live steers that are “finished” (fed to the appropriate weight) and ready to be slaughtered. Although the live cattle contract does not specify a weight range, finished steers typically weigh around 1,250 lbs. 2 A note on terminology is appropriate here. Curiously, there is no singular form of the word “cattle” in the English language that does not refer to a specific sex. Thus, I have chosen to use one feeder steer as the subject of my model illustration. Cattle that have not yet reached slaughter weight (approximately 1,250 lbs.) are typically called either feeder cattle (if 650 lbs. or heavier) or stocker cattle (if less than 650 lbs.). Feeder and stocker cattle are typically sold as either steers (castrated males) or heifers (females that have not yet given birth to a calf), although are bulls (males that have not been castrated) are commonly sold in some regions. The model presented here applies to heifers and bulls as well as steers.
3
is exogenous to the model, and the supply of live cattle. The beef production process is
characterized by long biological lags. This means that the current supply of live cattle for
slaughter is comprised of cattle that were born over 18 months earlier. Consequently, the future
supply of live cattle can be predicted well in advance of delivery based on current cattle
inventories. In this model I assume that cattle gain weight and progress through the beef
production and feeding process at a known constant rate. Thus, the supply of cattle in any given
weight group today will be equal to the supply of live cattle on the known future date when they
will all reach 1,250 lbs. This implies that current cash cattle prices for lighter weight animals are
linked to market conditions that are reflected in prices for heavier animals to be delivered in the
future.
Derived demand for the steer input in the two-input model can be obtained by subtracting
the cost of the corn feed input from the value of the finished 1,250 lb. steer output (following
Friedman 1962, chapter 7). The difference between the total value of the finished steer and the
total value of the input steer will be equal to the corn feed input cost. This difference is
commonly known as the gross feeding margin (GFM).
Example Feeder Cattle Model Calculations
An example using specific values for production coefficients, prices, and input variables
helps to illustrate the price slide relationship implied by the two-input derived demand model.
Table 1 displays feed requirement and cost calculations for two different weights of input steer: a
750 lb. “feeder” and a 550 lb. “stocker.” The calculations use a standard feed conversion factor
– seven pounds of corn grain are required to produce one pound of steer weight gain.3 Gray-
shaded values for input and output weights and corn prices (set initially at $7.50/bushel) are
considered to be exogenous. Since feed costs are linear with respect to weight, gross feeding
margin (GFM) is proportional to the weight of the input steer and per pound cost of gain (COG)
is equal for both steer types.
Derived values for the two weights of input steer are displayed in table 2. These are
calculated by subtracting the expected gross feeding margin calculated in table 1 from the
expected value of a finished 1,250 lb. steer. A live cattle futures price (LC1250) of $1.24 per
pound is used to calculate slaughter value for both weights of cattle in this example.
3 This conversion factor is common in the industry literature. See, for example, Anderson and Trapp 2000. Also note that one bushel of corn weighs 56 lbs.
4
Note that additional pounds of weight gain will always translate into greater value for
heavier steers in the two-input derived demand model as long as cost of gain is non-zero. At the
same time, we can see that the per pound price of a steer declines as sale weight increases. The
empirical analysis focuses on dynamics of the per pound price-weight relationship (the cattle
price slide).
Figure 1 plots calculated values from the two-input derived demand model over a
spectrum of input steer weights ranging from 200 to 1,250 lbs. using example price and
production input values. The required gross feeding margin declines with input weight starting
from approximately $1,000 GFM for a 200 lb. steer input. Steer input value increases linearly at
the same rate until steer input weight equals slaughter weight, GFM is zero, and the steer input
value equals slaughter value (Value_1250). The implied per pound price for each weight of steer
input is also plotted on the right vertical axis. Note that the model parameters used in this
example produce a downward sloping price slide relationship with a convex curvature.
This numerical example is also useful for illustrating the effect of corn input price on
both steer input value and the price slide. Figure 2 plots new model outputs calculated using
identical values for all parameters except the corn price, which has been reduced from $7.50 to
$3.50 per bushel. Holding all else equal, including the price of live cattle, a sharp reduction in
the price of corn lowers the GFM and raises the value of the input steer at all weights. In
addition, the slope of the price slide becomes steeper (more negative) over the entire range of
input steer weights.
Figure 3 depicts a familiar representation of the derived demand model using supply and
demand graphs. Here, V1250 represents the final output “price” (value per 1,250 lb. steer) that is
determined at the intersection of supply and final output demand. Since the quantity of steers
available for slaughter today were born months earlier and few alternative uses exist, the short-
run supply is assumed to be fixed (vertical supply curve). The gross feeding margin can also be
interpreted as the marginal cost or supply curve for the feed input, which I assume does not
depend on the quantity of steers (horizontal marginal cost curve). The derived demand for steers
as inputs can be obtained as the difference between the final output demand curve for 1,250 lb.
steers and the supply curve for feed inputs.
Graphing derived demand relationships normally requires that the input and output goods
be converted into equivalent units. However, in this case one unit of the steer input is
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necessarily equal to one unit of the slaughter steer output. Further, if we think of figure 3 as a
timeless representation of derived demand for a single group of steers moving between weight
ranges, then the supply of steer inputs at each weight must remain constant and equal to the final
output supply of slaughter steers. Thus, the value (price per steer) of a steer input is determined
at the intersection of a single vertical supply curve and a derived demand curve that corresponds
to the input weight. Consistent with the previous example calculations, value per steer increases
and per pound price decreases with steer input weight. The group of 550 lb. steers (valued at
$893.75/steer and $1.63/lb.) in figure 3 will become the 750 lb. feeder steers (valued at
$1,081.25/steer and $1.44/lb.) approximately three months later and become 1,250 lb. slaughter
steers (valued at $1,550/steer and $1.24/lb.) in roughly one year. Analysis of cattle prices at
different weights must therefore incorporate future price expectations for a particular weight
cohort of cattle.
Predictions about the shape of the price slide that have been derived from this two-input
derived demand model cannot be applied to a cross-section of prices for cattle of different
weights at a given point in time. This is because supply and demand conditions are likely to vary
for different cattle weight groups due to factors such as seasonality and cattle production trends.
Differences in inventory for different steer weights will affect supply in the final slaughter steer
output market and thus impact the derived demand price of steer inputs.
Figure 4 illustrates this point using separate derived demand markets for the 550 lb.
stockers and 750 lb. feeder steer inputs. The market for 550 lb. steers shown on the left is
identical to figure 3. However, the market shown in the panel on the right shows a larger supply
of 750 lb. feeder steers. Both input and output prices for the 750 lb. steer are lower relative to
the market conditions shown in figure 3 when a smaller quantity of steers was supplied. (For
reference, the supply curve and prices from figure 3 are shown by dashed lines in figure 4.)
Notice that the value of a 750 lb. feeder steer input in figure 4 is less than the value of the 550 lb.
stocker steer. This results directly from the lower expected live cattle price for the weight cohort
due to greater supply expectations.
This example clearly illustrates why a cross-section of prices for cattle of different sale
weights at a given point in time need not necessarily exhibit a downward-sloping price slide
relationship. Similar outcomes can be shown to result from differences in future demand for
slaughter steers. Because live cattle futures prices depend on expected supply and demand
6
conditions for a particular weight cohort of cattle, it will be important to link current cash
transactions to appropriate future price expectations in the empirical analysis.
III. Empirical Predictions
I use the two-input derived demand model to generate empirical predictions related to the
shape and dynamics of the price slide relationship. A mathematical representation of the model
facilitates the derivation of comparative static relationships.4 Recalling that the value of the
output is comprised of the combined value of both inputs, we begin with the following
expression:
1250
1250 *1250 * (1250 )InputWt InputWt
InputWt
Value Value GFMP P InputWt COG InputWt
= +
= + − (1)
I have assumed that the weight of the slaughter steer is fixed at exactly 1,250 lbs. as
described previously. InputWt is the weight of the steer at the time it is sold as a feeder cattle
input, and P always refers to a per pound price that is denoted by a subscript to identify the
weight of cattle for which the price pertains. COG is per pound cost of gain, which I assume to
be constant over all weight ranges and to depend only on the cost of the feed corn input, and
GFM refers to gross feeding margin based on steer input weight. Rearranging this relationship
gives us the price of the steer input in terms of known weights and exogenously determined
output and corn prices.
12501250 1250 1InputWtP P COG
InputWt InputWt
= − −
(2)
We further isolate the per pound price spread at different sale weights by expressing this
relationship in terms of the difference between input and output prices:
( ) ( )1250 12501250 1InputWtP P P COG
InputWt
− = − −
(3)
4 The mathematical model used here to develop of empirical predictions is similar to those used by Buccola (1980) and Ehrich (1969).
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Given that input steers must gain weight before slaughter and 1250InputWt < , we know
that the term in brackets must be positive. Therefore, the model predicts that price of the lighter
input steer will always be greater than the live cattle price ( 1250InputWtP P> ) when per pound price
of the output steer exceeds the marginal per pound cost of gain ( 1250P COG> ). This implies that
the price slide will be negatively sloped (as expected) except in cases where feed costs become
exceptionally high relative to live cattle prices.
For the empirical analysis I normalize the dependent variable to remove variation in
overall price levels and focus more directly on differentials between prices for different weights
of cattle. This normalization is accomplished by replacing the cash price of the input steer,
InputWtP , with basis to the feeder cattle contract, 750750InputWt InputWtBasis P P= − . By substituting for the
price of a 750 lb. steer and again rearranging the expression, I obtain the following equation for
feeder cattle basis:
( ) ( )750750 1250
750 12501750InputWt InputWtBasis P P P COG
InputWt = − = − −
(4)
This basis equation relates directly to an empirical strategy that predicts basis as the
dependent variable using sale weights, live cattle prices, and corn prices as explanatory variables.
Empirical predictions can now be generated by deriving comparative statics from feeder cattle
basis relationship. First derivatives with respect to the three explanatory variables are shown
below.
( )750
1250 2
750 1250750
InputWtBasisP COG
InputWt InputWt∂ = − − ∂
(negative*) (5.a)
750 750 12501750
InputWtBasisCOG InputWt
∂ = − − ∂ (negative) (5.b)
750
1250
750 12501750
InputWtBasisP InputWt
∂ = − ∂ (positive) (5.c)
The expected sign of each derivative is given in parentheses. Note that model predictions
for the impact of both cost of gain (negative) and live cattle price (positive) on the magnitude of
basis are unambiguous. However, the asterisk (*) next to the predicted sign of the first partial
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with respect to weight indicates that the slope of the price slide (expressed here in terms of basis)
will be negative only when 1250P COG> .
As shown previously, our model implies a quadratic price slide relationship. Taking the
second derivative with respect to weight allows us to sign the quadratic term.
( )2 750
12502 3
750 1250750
InputWtBasisP COG
InputWt InputWt∂ = − ∂
(positive*) (6.a)
The positive expected sign of the expression in equation (6.a) suggests that the price slide will
have a negative slope which becomes less negative (flattens) as weight of the input steer
increases. Cross-partial derivatives with respect to weight and prices yield two additional
predictions about dynamics of the price slide relationship that will be of particular interest for the
empirical analysis.
2 750
2
750 1250750
InputWtBasisCOG
InputWt COG InputWt∂ = ∂ ⋅∂
(positive) (6.b)
2 750
1250 21250
750 1250750
InputWtBasisP
InputWt P InputWt∂ = − ∂ ⋅∂
(negative) (6.c)
Two unambiguous model predictions are evident based on the sign of these expressions.
First, an increase in COG will cause the slope of the price slide to flatten (become less negative).
This implies that prices (and feeder cattle basis) for lighter weights of cattle will decline
disproportionately relative to heavier cattle. Second, an increase in the expected live cattle
output price will have the opposite effect: the slope of the price slide will increase as the prices
of lighter cattle increase relative to prices of heavier cattle.
IV. Data
This analysis makes use of an extensive database of cash cattle transactions obtained
from the USDA’s Agricultural Marketing Service (AMS). The AMS feeder cattle data include
information about all individual lots (sale groups) of cattle sold at hundreds of public auction
locations in more than 20 states across the continental U.S. In its entirety, the database contains
over 13 million sales transactions for cattle weighing between 300 and 900 pounds from 1996 to
9
2013. The cattle sold represent a variety of stages in the beef production process, from light
stockers to heavy feeders, although buyer information and intended use is not available.
A subset extracted from the larger AMS dataset has been used to conduct the preliminary
empirical analysis described in this working paper. The sample data contains 282,152
transactions from seven public auction locations in Kansas over a 10 year period. Each sales
transaction record in the dataset contains the date of sale, cash price, and several individual lot
characteristics. Lot characteristics about the group of cattle sold in each transaction include the
sales location, number of cattle in the group (lot size), average weight, and sex of the cattle
(steers, heifers, or bulls).
The AMS cash feeder cattle market data has been combined with CME futures price data.
Relevant cattle futures contracts were identified for each group of cattle sold, and prices were
linked to each transaction in the database. Sale date and average lot weight were used to
establish the future dates on which cattle in each sale lot would be predicted to attain weights of
750 and 1,250 pounds assuming a constant rate of weight gain. These weights were chosen
because they correspond to weight specifications for the feeder and live cattle futures contracts,
respectively.
As a specific example, consider a lot of cattle sold on 10/1/2012 with an average weight
of 550 lbs. Assuming average gain of 2 lbs. per day, these cattle would be expected to weigh
750 lbs. after 100 days on January 9, 2013. As of that date, the JAN2013 feeder cattle contract
would be next to expire (nearby contract) on 1/31/2013. The same group of cattle would be
expected to weigh 1,250 pounds after another 250 days ((1,250 lbs. – 750 lbs.) / 2 lbs./day) on
9/16/2013 when the OCT2013 live cattle contract would be next to expire on 10/31/2013. The
observed daily settlement prices for these contracts on 10/1/2013 determine the values of feeder
cattle and live cattle price variables for the cattle:
itFC750 = Price of JAN2013 feeder cattle contract on 10/1/2012 = $148.125 /cwt
itLC1250 = Price of OCT2013 live cattle contract on 10/1/2012 = $133.75 / cwt
These prices are subscripted for sale date t and individual lot i. They reflect the expected
future supply and demand conditions for a specific group of cattle described in the sales
transaction. In a broader sense, these are specific market price expectations for a single weight
cohort of cattle that are assumed to reach slaughter weight at the same time. For empirical
10
estimation, itFC750 is used as the current estimate of 750P (the expected future price of the group
of cattle at 750 lbs.) and itLC1250 is used as the current estimate of 1250P (the expected future
price of the group of cattle at 1,250 lbs.). Current basis is calculated using the feeder cattle
contract reference price of itFC750 for each cattle sales transaction as follows:
750it it itBasis Cash FC750= − (7)
The current price of the nearby corn contract, tCN0 , proxies for feed input costs in the
empirical model. For lighter weight animals, prices of deferred corn futures contracts (contracts
expiring after the nearby) might also be considered. However, the nearby contract price was
chosen as the best corn price expectation at all sale weights for two reasons: 1) remaining feed
input requirements are easily forecast in advance based on the average weight of the group of
cattle purchased, and 2) corn for grain is a storable commodity. Together, these imply that a
cattle buyer will always have the option of purchasing the expected feed corn requirement at the
same time as the cattle.
Table 4 displays summary statistics for the sample Kansas dataset that was used in the
empirical analysis. These data span a period from January 6, 1999 to March 26, 2009 and
include data for sale lots of feeder and stocker cattle weighing 300 to 900 pounds. The time
period also included substantial variation in the prices of feeder cattle ($69.97 to $119.57 per
cwt), live cattle ($60.67 to $117.70 per cwt), and corn ($1.75 to $7.61 per bushel). Feeder cattle
basis in the sample data ranged from a low of -$63.62 (when cash price was lower than FC750)
to a high of $87.33.
V. Estimation and Results
To test predictions developed from the two-input derived demand model, I estimate a
hedonic regression of feeder cattle basis. My analysis focuses primarily on the price relationship
between cattle basis and weight, as described previously. The basic regression specification in
Model 1 below describes this relationship and accommodates an expected quadratic shape for the
price slide.
Model 1: 750 2* *it it it itBasis a b Weight c Weight ε= + + +
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The expected shape of the price slide relationship from figures 1 and 2 suggest that a and c will
be positive, while b should be negative. Our model also generated predictions about the
relationship between basis and expected prices for the live cattle output and feed corn input.
Model 2 gives another simple linear specification that includes these variables of interest:
Model 2: 750 2* * * 0 * 1250it it it t it itBasis a b Weight c Weight d CN e LC ε= + + + + +
Comparative statics derived previously predicted that the sign on coefficient d will be negative
and coefficient e will be positive. Parameter estimates for models 1 and 2 are shown in table 5.
All four coefficients exhibit the predicted signs in both models and are highly significant (p-
values < 0.0001).
Models 1 and 2 generate parameter estimates that can be easily interpreted and directly
compared to model predictions. However, these simple specifications have some obvious
limitations. In particular, they do not facilitate testing of any dynamic interaction between
market prices and weight. To explore these relationships requires the introduction of additional
interaction terms between weight and price. Model 3 allows the slope of the price slide to
depend on expected corn and live cattle prices.
Model 3:
( )( )
750
2
2
* 0 * 1250 * 0 * 1250 *
* 0 * 1250 *
* * * 0 * 1250 * 0 * * 1250 *
it t it
t it it
t it it it
it it t it
t it it it
Basis a d CN e LCb f CN g LC Weight
c h CN l LC Weight
a b Weight c Weight d CN e LCf CN Weight g LC Weight
ε
= + +
+ + +
+ + + +
= + + + ++ +
2 2 * 0 * * 1250 *t it it it ith CN Weight l LC Weight ε+ + +
Interpreting the meaning of coefficients estimated from Model 3 within the context of
previously derived predictions requires that we first take derivatives of the regression equation.
First, second, and cross-partial derivatives of basis with respect to the independent variables of
Model 3 are shown below, followed by their predicted signs.
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First derivatives:
( )
( )
750
* 0 * 1250
2* * 0 * 1250 *
InputWtt it
t it it
Basisb f CN g LC
Weightc h CN l LC Weight
∂= + +
∂
+ + +
(negative*) (8.a)
7502* *
0InputWt
it itt
Basisd f Weight h Weight
CN∂
= + +∂
(negative) (8.b)
7502* *
1250InputWt
it itit
Basise g Weight l Weight
LC∂
= + +∂
(positive) (8.c)
Second and cross partial derivatives:
( )2 750
2 2* * 0 * 1250InputWtt it
Basisc h CN l LC
Weight∂
= + +∂
(positive*) (9.a)
2 750
2* *0
InputWtit
t
Basisf h Weight
Weight CN∂
= +∂ ⋅∂
(positive) (9.b)
2 750
2* *1250
InputWtit
it
Basisg l Weight
Weight LC∂
= +∂ ⋅∂
(negative) (9.c)
Equations (8.a) – (8.c) and (9.a) – (9.c) are empirical counterparts to (5.a) – (5.c) and
(6.a) – (6.c), respectively. These derivatives must be evaluated at specific values of the
explanatory variables to determine their sign. The relationships are consistent with the
comparative static results. First and second partials of basis with respect to weight depend on
exogenous corn and live cattle prices and sale weight. The predicted sign of these derivatives
also depends on the relative per pound price of gain and slaughter cattle. First partials and cross-
partials with respect to both prices also exhibit consistency with the comparative static results in
the sense that they depend only on weight. These maintain their predicted sign when sale weight
is at or below the feeder cattle weight of 750 lbs.
The plots in figure 5 show predicted values of the dependent variable, 750InputWtBasis , and the
partial derivative relationships from Model 3. Predicted values are calculated at mean values of
the live cattle and corn price variables and plotted against weight. These graphs make it visually
apparent that the slope of the price slide (8.a) becomes more steep (negatively sloped) at lighter
sale weights. An increase in the corn price produces a decrease in basis at all weights (8.b) and
“flattens” the negative slope of the price slide to a greater degree at lighter weights (9.b).
Similarly, live cattle price increases increase basis at all weights (8.c) and increase the
“steepness” of the price slide to a greater degree for lighter cattle.
13
In order to more easily interpret and visualize the price slide dynamics, figures 6 and 7
plot predicted basis from Model 3 at different values of the corn an live cattle price. The price
slide shown in the middle of both figures plots basis predictions at the sample mean values of
both price variables (equivalent to figure 5). In figure 6, the corn price is held constant and two
additional predictions are plotted for the live cattle price at one standard deviation above and
below the sample mean of $78.33/cwt. Figure 7 holds live cattle price constant and plots
predictions for corn prices one standard deviation above and below the mean value of
$2.61/bushel. These figures clearly show the manner in which changes in live cattle and corn
prices make the price slide steeper or flatter and have larger impacts on the price slide at lighter
cattle weights.
Lot Characteristics
Several previous studies have demonstrated the importance of other lot characteristics in
determining feeder cattle prices and basis. I control for and test the significance of several lot
characteristics by adding them as additional explanatory variables in models 2 and 3. Table 5
displays estimates for the price and weight variables when other lot characteristics are included
as Model 2(o) and Model 3(o). Coefficients for individual lot characteristics are suppressed. A
comparison of estimated parameters from models with and without lot characteristics is
informative. Most notably, the inclusion of lot characteristics produces a considerable
improvement in the adjusted R-square for both models, suggesting that these factors are indeed
important basis determinants. Further, the inclusion of lot characteristics does not cause
appreciable change in the values of any of the price-weight coefficients.
Coefficients for the individual lot characteristic variables from the Model 3(o)
specification are displayed separately in table 6. All of these estimates exhibit strong statistical
significance, which is not surprising in light of the large number of observations. The sign of the
coefficient on lot size is consistent with many previous studies (for example Dhuyvetter and
Schroeder, 2000), which have shown that larger groups of cattle sell at a premium compared to
smaller lots. Dummy variables were included for four additional characteristics: sex, class,
month, and location. The estimates suggest that buyers pay a premium for steers relative to
heifers or bulls and for cattle grading at class 1. Monthly dummy variables capture seasonal
price differences and show that basis is lowest for feeder cattle that are sold in the fall months.
This is consistent with previous research and also consistent with the notion that a large supply
14
of spring calves results in a large supply of fall stocker cattle. Location dummies reveal that
basis also differs based on where the cattle are sold. This might result from geographic price
differences as well as from differences in the type of cattle that are sold at different auction
locations.
VI. Conclusions and Future Research
The research presented in this working draft has demonstrated that empirical
relationships between price and weight are consistent with predictions derived from a simple
two-input derived demand model. Dynamics of the cattle price slide are clearly linked to
changing conditions in the markets for corn feed inputs and live cattle outputs. Further, these
relationships depend on future expectations of prices for cattle at different sale weights.
Information about expected future market conditions for specific groups of cattle was
incorporated by identifying appropriate futures contract prices.
The preliminary empirical analysis presented here suggests many possible areas for
future exploration. For example, several explanatory variables could potentially be added to the
model. These might include proxies for pasture feed inputs (ex., Palmer drought index), cattle
inventory numbers, fuel costs, and recent feedlot profit margins. I also plan to consider the
potential for additional dynamic interactions between the price slide and market or lot
characteristics. Future empirical analysis will include more extensive treatment of
contemporaneous corn and live cattle price relationships. In particular, I will explore whether
high corn prices in recent years may have caused the price slide relationship to invert at certain
points in time.
Most obviously, the analysis will be expanded to include a vast AMS database of feeder
cattle transactions. This introduces regional variation in price slide dynamics that might stem
from proximity to corn production and feedlot facilities or from regional differences in
production practices and types of animals sold. Expanding the dataset will also introduce
additional intertemporal variation by the inclusion of recent years with high and variable prices.
I will look to exploit this substantial variation and contribute to the understanding of price slide
dynamics.
15
References
Anderson, J.D. and J.N. Trapp. 2000. “The Dynamics of Feeder Cattle Market Responses to Corn Price Change.” Journal of Agricultural and Applied Economics 32: 493-505.
Buccola, S.T. 1980. “An Approach to the Analysis of Feeder Cattle Price Differentials.” American Journal of Agricultural Economics 62: 574-580.
Dhuyvetter, K.C. and T.C. Schroeder. 2000. “Price-Weight Relationships for Feeder Cattle.” Canadian Journal of Agricultural Economics 48: 299-310.
Dhuyvetter, K.C., K. Swanser, T. Kastens, J. Mintert and B. Crosby. 2008. “Improving Feeder Cattle Basis Forecasts.” Western Agricultural Economics Association Selected Paper.
Ehrich, R.L. 1969. “Cash-Futures Price Relationships for Live Beef Cattle.” American Journal of Agricultural Economics 51: 26-40.
Friedman, M. 1962. Price Theory. Aldine Publishing Co., Chicago, IL. Marsh, J.M. 1985. “Monthly Price Premiums and Discounts Between Steer Calves and
Yearlings.” American Journal of Agricultural Economics 67: 307-314.
Schroeder, T.C., J.R. Mintert, F. Brazle and O. Grunewald. 1988. “Factors Affecting Feeder Cattle Price Differentials.” Western Journal of Agricultural Economics 13: 71-81.
16
Table 1. Example feed cost calculations for two weights of the steer input
Table 2. Example derived steer input values and prices
Table 3. Summary of example steer prices by weight
Feeder StockerOutput (slaughter) weight 1250 1250 lbs- Input Weight 750 550 lbsGain Required 500 700 lbsx Corn Conversion 7 7 Corn Input (lbs) 3,500 4,900 lbs÷ corn bushels / lb 56 56 Corn Input (bushels) 62.5 87.5 bushelsx Corn Price ($/bushel) 7.50$ 7.50$ per bushelGross Feeding Margin (GFM) 468.75$ 656.25$ per headCost of Gain (COG) 0.94$ 0.94$ per lb
Price_LC1250 1.24$ 1.24$ per lbx Weight_1250 1250 1250 lbsSlaughter value 1,550.00$ 1,550.00$ $/hd- GFM 468.75$ 656.25$ $/hdSteer Input Value (derived) 1,081.25$ 893.75$ $/hd÷ steer input weight 750 550 lbsSteer Input Price (derived) 1.44$ 1.63$ per lb
Steer type Weight Price ValueSlaughter 1250 1.24$ 1,550.00$ Feeder 750 1.44$ 1,081.25$ Stocker 550 1.63$ 893.75$
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Table 4. Summary statistics for Kansas sample data
Number of observations = 282,152Variable Description Units Mean Std Dev Minimum MaximumSaleDate YYYYMMDD 20031370.7 29550.4 19990106 20090326
Year YYYY 2003 2.9566456 1999 2009Weight Sale weight pounds 648.1 141.2 300 900
Price VariablesBasis750
it [Cash price] - [FC750] $/cwt 2.48 10.42 -63.62 87.33
Cash Price Cash sale price $/cwt 95.17 16.30 34.75 199.00FC750 Price on sale date for feeder cattle
futures contract that will be nearby when cattle weigh 750 lbs
$/cwt 92.32 12.52 69.97 119.57
CN0 Price on sale date for nearby corn futures contract price
$/bushel 2.61 0.91 1.75 7.61
LC1250 Price on sale date for live cattle contract that will be nearby when cattle weigh 1250 lbs
$/cwt 78.33 10.37 60.67 117.70
Interaction/Quadratic TermsWt2 439982.46 178863.47 90000 810000
CN0*Wt 1697.02 732.742102 525.75003 6810.95LC1250Wt 50843.18 13373.13 19740 100598CN0*Wt2 1156605.42 664827.73 157725.01 6095800.33
LC1250Wt2 34561057.4 15142460.1 5922000.3 90336666.8Lot Characteristics
Lot Size # head sold 25.0325959 64.7853519 1 3600Str Steers 0.5334784 0.4988788 0 1Hfr Heifers 0.463587 0.4986732 0 1Bul Bulls 0.0029346 0.0540924 0 1
Class1 Class 1 0.6654108 0.4718475 0 1Class12 Class 1-2 0.1944413 0.3957707 0 1Class2 Class 2 0.1357035 0.342474 0 1Mo1 January 0.1168555 0.3212485 0 1Mo2 February 0.0929889 0.2904174 0 1Mo3 March 0.1228026 0.3282111 0 1Mo4 April 0.1015233 0.3020209 0 1Mo5 May 0.0651351 0.2467645 0 1Mo6 June 0.0254225 0.1574047 0 1Mo7 July 0.0492749 0.2164417 0 1Mo8 August 0.0757393 0.264581 0 1Mo9 September 0.0703734 0.2557757 0 1
Mo10 October 0.1130136 0.3166099 0 1Mo11 November 0.1056452 0.3073835 0 1Mo12 December 0.0612259 0.2397446 0 1Loc01 Syracuse, KS 0.0378413 0.1908127 0 1Loc02 Junction City, KS 0.0776993 0.2676982 0 1Loc03 Winter Livestock Video 0.0017508 0.0418063 0 1Loc04 Winter Livestock Auction 0.1928039 0.3945011 0 1Loc05 Pratt Livestock Auction 0.265917 0.441821 0 1Loc06 Kansas Direct Feeder Cattle 0.0553957 0.2287513 0 1Loc07 Farmers & Ranchers Lvstk Co 0.3685921 0.4824239 0 1
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Table 5. Model parameter estimates for price-weight variables
Dependent Variable = Basis750it
Number of observations = 282,152Parameter Model 1 Model 2 Model 2(o) Model 3 Model 3(o)Adj. R-square 0.4834 0.4887 0.7438 0.5096 0.7581a Intercept 66.83442 64.01814 54.13294 -94.74554 -82.56878
(0.25949) (0.28440) (0.21004) (2.32976) (1.64035)257.56 225.10 257.73 -40.67 -50.34
b Weight -0.15744 -0.15813 -0.12886 0.2677 0.24727(0.00084697) (0.00084271) (0.00060393) (0.00747) (0.00526)
-185.89 -187.64 -213.37 35.84 47.01c Wt2 0.000085666 0.00008634 0.00005586 -0.00018488 -0.0001905
(6.686718E-07) (6.653638E-07) (4.789582E-07) (0.00000580) (0.00000408)128.11 129.76 116.63 -31.88 -46.69
d CN0 -1.27259 -2.23911 -27.73627 -25.64551(0.2355) (0.01743) (0.45203) (0.31815)
-5.40 -128.46 -61.36 -80.61e LC1250 0.08021 0.19665 2.99828 2.73032
(0.00206) (0.00158) (0.04014) (0.02827)38.94 124.46 74.70 96.58
f CN*Wt 0.07012 0.06225(0.00144) (0.00101)
48.69 61.63g LC1250*Wt -0.0078 -0.0069
(0.00012775) (0.00008997)-61.06 -76.69
h CNWt2 -0.00004417 -0.00003922(0.00000111) (7.813848E-07)
-39.79 -50.19l LC1250Wt2 0.00000495 0.00000447
(9.863877E-08) (6.943237E-08)50.18 64.38
Lot Characteristics Included Included
Notes: Estimated coefficients (standard errors) and t-statistics are shown. All estimates are statistically significant with P-values <0.0001. Individual parameter estimates for lot characteristics included in models 2(o) and 3(o) have been suppressed.
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Table 6. Individual parameter estimates for lot characteristics - Model 3(o)
Dependent Variable = Basis750it
Number of observations = 282,152Parameter Estimate (StdErr) T-stat# Head Sold (Lot Size) 0.00169 (0.00017732) 9.53Sex Dummies
Steer 0Heifer -8.14089 (0.01982) -410.74Bull -6.88621 (0.17916) -38.44
Class DummiesClass1 0Class12 -4.18968 (0.02570) -163.02Class2 -7.0359 (0.02988) -235.47
Month DummiesJanuary 4.00651 (0.04096) 97.82February 5.37661 (0.04361) 123.29March 5.7799 (0.04084) 141.53April 6.73215 (0.04242) 158.70May 5.35235 (0.04830) 110.81June 4.13316 (0.06803) 60.75July 4.48984 (0.05262) 85.33August 3.76185 (0.04575) 82.23September 2.22642 (0.04654) 47.84October 0November 0.8747 (0.04143) 21.11December 3.0218 (0.04861) 62.16
Location DummiesSyracuse, KS -2.27804 (0.05340) -42.66Junction City, KS -0.85572 (0.03909) -21.89Winter Livestock Video -3.87664 (0.23314) -16.63Winter Livestock Auction -1.32923 (0.02758) -48.20Pratt Livestock Auction -0.66062 (0.02537) -26.04Kansas Direct Feeder Cattle -1.61017 (0.05248) -30.68Farmers & Ranchers Lvstk Co 0
Notes: Estimated coefficients (standard errors) and t-statistics are shown. All estimates are statistically significant with P-values <0.0001. Price and weight coefficients shown on table 5.
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Figure 1. Example value, price, and feed cost calculations by steer input weight
Figure 2. Example calculations with reduced corn price
Value_1250 = $1,550.00 P_1250 = LC1250 = $1.24/lb Corn Price = $7.50/bu
Price slide ($/lb)
Value ($/ hd)
Value_750 = $1,081.25 Price_750 = $1.44/lb.
P_1250 = LC1250 = $1.24/lb Corn Price = $3.50/bu
GFM ($7.50/bu) # of days needed to reach 1250 lbs.
Value_1250 = $1,550.00
Value ($/ hd)
Price slide ($/lb) Value_750 = $1,331.25 Price_750 = $1.78/lb
GFM ($3.50/bu)
# of days needed to reach 1250 lbs.
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Figure 4. Example Derived Demand for Stocker and Feeder Steers with Different Quantities of Future Supply